for some function of time \(\delta (\eta )\)  that encodes the difference from GR. One can then show that, while in GR the signal from a coalescing binary allows the extraction of the luminosity distance of the source, in the context of modified gravity it rather provides a determination of a different
quantity, \(d_L^{\,\rm gw}(z)\) , called the “GW luminosity distance" [1]}. This is related to the standard luminosity distance [that, in this context, we call the `electromagnetic luminosity distance' and denote by \(d_L^{\,\rm em}(z)\) ] by [1]}, [3]}
\(d_L^{\,\rm gw}(z)=d_L^{\,\rm em}(z)\exp \left\lbrace -\int _0^z \,\frac{dz^{\prime }}{1+z^{\prime }}\,\delta (z^{\prime })\right\rbrace \, ,\) 
